Which spatial interpolators I should use? A case study applying to marine species

Abstract

Species are spread in space, whereas sampling is sparse. Thus, to describe and map along environmental gradients, it is necessary to interpolate the species abundance. Considering the plethora of valid methods, the researcher gets easily puzzled to choose the most appropriate interpolation approach with reference to the ecological question being asked.We propose a procedure to select among alternative spatial distribution models and we illustrate it with 175 marine species distributions (35 species * 5 years). In a first step, the distribution of the variance explained by the predictive model (VEcv) given by 10-fold cross validation is estimated for each interpolation method. When the inter-quartile range of the VEcv distribution of the different methods overlap, the selection passes to a second step, using 11 measures belonging to three criteria: 1) error based measures, 2) spatial equivalence measures (center of gravity, inertia, isotropy and index of aggregation) and 3) measures based on the data integrity after interpolation, for example the percentage of area over the maximum sampled data.We applied our approach to marine species sampled using either stratified random survey (trawl) or systematic survey (acoustic). We found that 87% of all species distributions had overlapping VEcv and thus passed the first selection. In the second selection step, the best method varied with species and year, although general additive model (GAM), Thin Plate Spline (TPS), Universal Kriging (UKr) and Random Forest (Rfor) performed better for the trawl data and TPS, Ordinary Kriging (OKri) and UKr for the acoustic data. Further, the results differed within methods (e.g. kriging neighborhood and type of kriging) and small modifications on the specifications can have a large impact on the surfaces produced.The proposed approach 1) is accessible and intuitive, and does not require any complex software or sophisticated methodology; 2) shows exactly in what aspects each interpolation model is prevalent over the others and permits to make a decision accordingly to the objectives of the study; 3) takes into account different criteria to evaluate each, properties of an interpolation method; 4) is universal and does not depend on the method used or the data characteristics. A detailed review on the subject is also included.